Question

What is the equation of the line perpendicular to y=2x+3.14 going through the points (2,4)?

Answer 1

`x+2y-10=0`

Explanation:

Consider an equation:
`y=mx+c`

Here, m is the slope of the line and c is the y-intercept.

Given equation is
`y=2x+3.14`

Here, slope is
`m=2`

As product of slopes of two perpendicular lines is equal to
`-1`, slope of the required line is
`m_1=(-1)/(m)=(-1)/(2)`.

Let
`(x_1,y_1)=(2,4)`

Equation of the required line is
`y-y_1=m_1(x-x_1)`

`y-4=(-1)/(2)(x-2)\\2(y-4)=-1(x-2)\\2y-8=-x+2\\x+2y-8-2=0\\x+2y-10=0`